A multi-objective multi-population ant colony optimization for economic emission dispatch considering power system security

With increasing concern about global warming and haze, environmental issue has drawn more attention in daily optimization operation of electric power systems. Economic emission dispatch (EED), which aims at reducing the pollution by power generation, has been proposed as a multi-objective, non-convex and non-linear optimization problem. In a practical power system, the problem of EED becomes more complex due to conflict between the objectives of economy and emission, valve-point effect, prohibited operation zones of generating units, and security constraints of transmission networks. To solve this complex problem, an algorithm of a multi-objective multi-population ant colony optimization for continuous domain (MMACO_R) is proposed. MMACO_R reconstructs the pheromone structure of ant colony to extend the original single objective method to multi-objective area. Furthermore, to enhance the searching ability and overcome premature convergence, multi-population ant colony is also proposed, which contains ant populations with different searching scope and speed. In addition, a Gaussian function based niche search method is proposed to enhance distribution and accuracy of solutions on the Pareto optimal front. To verify the performance of MMACO_R in different multi-objective problems, benchmark tests have been conducted. Finally, the proposed algorithm is applied to solve EED based on a six-unit system, a ten-unit system and a standard IEEE 30-bus system. Simulation results demonstrate that MMACO_R is effective in solving economic emission dispatch in practical power systems.     

A new multiobjective procedure for solving nonconvex environmental/economic power dispatch

In this article, an improved multiobjective chaotic interactive honey bee mating optimization (CIHBMO) is proposed to find the feasible optimal solution of the environmental/economic power dispatch problem with considering operational constraints of the generators. The three conflicting and noncommensurable: fuel cost, pollutant emissions, and system loss, should be minimized simultaneously while satisfying certain system constraints. To achieve a good design with different solutions in a multiobjective optimization problem, Pareto dominance concept is used to generate and sort the dominated and nondominated solutions. Also, fuzzy set theory is used to extract the best compromise solution. The propose method has been individually examined and applied to the standard Institute of Electrical and Electronics Engineers (IEEE) 30‐bus six generator, IEEE 180‐bus 14 generator and 40 generating unit (with valve point effect) test systems. The computational results reveal that the multiobjective CIHBMO algorithm has excellent convergence characteristics and is superior to other multiobjective optimization algorithms. Also, the result shows its great potential in handling the multiobjective problems in power systems. © 2014 Wiley Periodicals, Inc. Complexity 20: 47–62, 2014     

Improved time varying inertia weight PSO for solved economic load dispatch with subsidies and wind power effects

This article presents a new approach to economic load dispatch (ELD) problems by the considering the cost functions, impact renewable energy as wind turbin and subsidies. Economic dispatch is the short‐term determination of the optimal output of a number of electricity generation facilities, to meet the system load, at the lowest possible cost, subject to transmission and operational constraints. The main goal in the deregulated system is subsidies and analysis performance on government to minimize the total fuel cost while satisfying the load demand and operational constraints. The practical ELD problems have nonsmooth cost functions with equality and inequality constraints, which make the problem of finding the global optimum difficult when using any mathematical approaches. Accordingly, particle swarm optimization with time‐varying inertia weight (PSO‐TVIW) used for solving this problem. The effectiveness of the proposed strategy is applied over real‐world engineering problem and highly constrained. Obtained results indicate that PSO‐TVIW can successfully solve this problem. © 2014 Wiley Periodicals, Inc. Complexity 21: 40–49, 2016     

安全约束条件下的经济调度优化模型研究

发电侧放开竞争的电力系统需要更加有效、准确的决策工具对有限的资源进行调度规划。短期经济调度优化问题是一个混合整数非线性规划问题,很难得到有效最优解,尤其是对于大规模电力系统。为了提高求解效率,本文提出了一个考虑安全约束的经济调度优化模型(Security-Constrained Economics Dispatch,SCED),主要采用线性化思想处理经济调度优化问题的模型以及各种约束,采用基于校正的交替求解方法,使得调度优化结果在运行成本最小化的前提下满足系统的安全稳定约束。同时,将本文方法运用到IEEE 30节点系统进行测试,从而验证本文方法有效性。     

A novel method for optimal capacitor placement and sizing in distribution systems with nonlinear loads and DG using GA

A genetic algorithm (GA) is proposed for simultaneous power quality improvement, optimal placement and sizing of fixed capacitor banks in radial distribution networks with nonlinear loads and distributed generation (DG) imposing voltage–current harmonics. In distribution systems, nonlinear loads and DGs are often considered as harmonic sources. For optimizing capacitor placement and sizing in the distribution system, objective function includes the cost of power losses, energy losses and capacitor banks. At the same time, constraints include voltage limits, number/size of installed capacitors (at each bus) and the power quality limits of standard IEEE-519. In this study, new fitness function is used to solve the constrained optimization problem with discrete variables. Simulation results for two IEEE distorted networks (18-bus and 33-bus test systems) are presented and solutions of the proposed method are compared with those of previous methods described in the literature. The main contribution of this paper is computing the (near) global solution with a lower probability of getting stuck at a local optimum and weak dependency on initial conditions, while avoiding numerical problems in large systems. Results show that proposed method could be effectively used for optimal capacitor placement and sizing in distorted distribution systems.     

Optimal discrete long-term operation of nuclear-hydrothermal power systems

We discuss in this paper an algorithm for solving the optimal long-term operating problem of a hydrothermal-nuclear power system by application of the minimum norm optimization technique. The algorithm proposed here has the ability to deal with large-scale power systems and with equality and/or inequality constraints on the variables. A discrete model for the xenon and iodine concentrations is used, as well as a discrete model for hydro reservoirs. The optimization is done on a monthly time basis. For simplicity of the problem formulation, the transmission line losses are considered as a part of the load.This work supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A4146.     

Dynamic economic dispatch using Lbest-PSO with dynamically varying sub-swarms

Dynamic economic dispatch (DED) is one of the major planning problem in a power system. It is a non-linear optimization problem with various operational constraints, which includes the constraints of the generators operating characteristics and the system constraints. Its principal aim is to minimize the cost of power production of all the participating generators over a time horizon of 24 h, while satisfying the system constraints. This problem deals with non-convex characteristics if generation unit valve-point effects are taken into account. The paper intends to solve the DED problem with valve-point effects, using our modified form of Local-best variant of Particle Swarm Optimization (Lbest PSO) algorithm. We have tested our algorithm on 5-unit, 10-unit and 110-unit test system with non-smooth fuel cost functions to prove the effectiveness of the suggested method over different state of the art methods.     

An efficient co-swarm particle swarm optimization for non-linear constrained optimization

This paper proposes a new co-swarm PSO (CSHPSO) for constrained optimization problems, which is obtained by hybridizing the recently proposed shrinking hypersphere PSO (SHPSO) with the differential evolution (DE) approach. The total swarm is subdivided into two sub swarms in such a way that the first sub swarms uses SHPSO and second sub swarms uses DE. Experiments are performed on a state-of-the-art problems proposed in IEEE CEC 2006. The results of the CSHPSO is compared with SHPSO and DE in a variety of fashions. A statistical approach is applied to provide the significance of the numerical experiments. In order to further test the efficacy of the proposed CSHPSO, an economic dispatch (ED) problem with valve points effects for 40 generating units is solved. The results of the problem using CSHPSO is compared with SHPSO, DE and the existing solutions in the literature. It is concluded that CSHPSO is able to give the minimal cost for the ED problem in comparison with the other algorithms considered. Hence, CSHPSO is a promising new co-swarm PSO which can be used to solve any real constrained optimization problem.     

Optimal placement and sizing of capacitor using Limaçon inspired spider monkey optimization algorithm

The power system is a complex interconnected network which can be subdivided into three components: generation, distribution, and transmission. Capacitors of specific sizes are placed in the distribution network so that losses in transmission and distribution is minimum. But the decision of size and position of capacitors in this network is a complex optimization problem. In this paper, Limaçon curve inspired local search strategy (LLS) is proposed and incorporated into spider monkey optimization (SMO) algorithm to deal optimal placement and the sizing problem of capacitors. The proposed strategy is named as Limaçon inspired SMO (LSMO) algorithm. In the proposed local search strategy, the Limaçon curve equation is modified by incorporating the persistence and social learning components of SMO algorithm. The performance of LSMO is tested over 25 benchmark functions. Further, it is applied to solve optimal capacitor placement and sizing problem in IEEE-14, 30 and 33 test bus systems with the proper allocation of 3 and 5-capacitors. The reported results are compared with a network without a capacitor (un-capacitor) and other existing methods.     

Optimal economic load dispatch based on wind energy and risk constrains through an intelligent algorithm

This article focus on optimal economic load dispatch based on an intelligent method of shark smell optimization (SSO). In this problem, the risk constrains has been considered which has root in uncertainity and unpredictable behavior of wind power. Regarding to increasing of this clean energy in power systems and un‐dispatchable behavior of wind power, its conditional value at risk index considered in this article which consists of loss from load and "spilling" wind energy connected with unpredictable imbalances among generation and load. This problem has been considered as an optimization problem based on SSO that evaluate the balance between cost and risk. This algorithm is based on distinct shark smell abilities for localizing the prey. In sharks' movement, the concentration of the odor is an important factor to guide the shark to the prey. In other words, the shark moves in the way with higher odor concentration. This characteristic is used in the proposed SSO algorithm to find the solution of an optimization problem. Effectiveness of the proposed method has been applied over 30‐bus power system in comparison with other techniques. © 2016 Wiley Periodicals, Inc. Complexity 21: 494–506, 2016     

A new two‐stage algorithm for solving power flow tracing

This article proposed a new hybrid algorithm for solving power flow tracing (PFT) through the comparison by other techniques. This proposed hybrid strategy in detail discuses over the achieved results. Both methods use the active and reactive power balance equations at each bus to solve the tracing problem, where the first method considers the proportional sharing assumption and the second one considers the circuit laws to find the relationship between power inflows and outflows through each line, generator, and load connected to each bus of the network. Both algorithms are able to handle loop flow and loss issues in tracing the problem. A mathematical formulation is also introduced to find the share of each unit in provision of each load. These algorithms are employed to find the producer and consumer's shares on the cost of transmission for each line in different case studies. As the results of these studies show, both algorithms can effectively solve the PFT problem. © 2014 Wiley Periodicals, Inc. Complexity 21: 187–194, 2015     

电网安全调度中输电阻塞管理的演化策略

输电阻塞是电力系统运行中的常见问题 .本文建立了用于电网安全调度中输电阻塞管理的数学模型——带线性约束的多目标模糊优化问题模型 ,给出了求解该模型的演化策略 .实际的计算结果表明 ,演化策略解决输电阻塞问题是有效的 .     

Hybrid harmony search algorithm and fuzzy mechanism for solving congestion management problem in an electricity market

A hybrid technique for solving the congestion management problem in an electricity market based on harmony search algorithm (HAS) and Fuzzy mechanism is presented in this article. This algorithm does not require initial value setting for the variables and does not require differential gradients, thus it can consider discontinuous functions as well as continuous functions. The HAS is a recently developed powerful evolutionary algorithm, inspired by the improvisation process of musicians, for solving single/multiobjective optimization problems. In the proposed technique, each musician plays a note for finding a best harmony all together. Transmission pricing and congestion management are the key elements of a competitive electricity market based on direct access. They also focus of much of the debate concerning alternative approaches to the market design and the implementation of a common carrier electricity system. This article focuses on the tradeoffs between simplicity and economic efficiency in meeting the objectives of a transmission pricing and congestion management scheme. The effectiveness of the proposed technique is applied on 30 and 118 bus IEEE standard power system in comparison with CPSO, PSO‐TVAC, and PSO‐TVIW. The numerical results demonstrate that the proposed technique is better and superior than other compared methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 90–98, 2016     

Limit vector variational inequality problems via scalarization

This paper presents a global optimization approach for solving signomial geometric programming (SGP) problems. We employ an accelerated extended cutting plane (ECP) approach integrated with piecewise linear (PWL) approximations to solve the global optimization of SGP problems. In this approach, we separate the feasible regions determined by the constraints into convex and nonconvex ones in the logarithmic domain. In the nonconvex feasible regions, the corresponding constraint functions are converted into mixed integer linear constraints using PWL approximations, while the other constraints with convex feasible regions are handled by the ECP method. We also use pre-processed initial cuts and batched cuts to accelerate the proposed algorithm. Numerical results show that the proposed approach can solve the global optimization of SGP problems efficiently and effectively.     

A smoothing augmented Lagrangian method for solving simple bilevel programs

In this paper, we design a numerical algorithm for solving a simple bilevel program where the lower level program is a nonconvex minimization problem with a convex set constraint. We propose to solve a combined problem where the first order condition and the value function are both present in the constraints. Since the value function is in general nonsmooth, the combined problem is in general a nonsmooth and nonconvex optimization problem. We propose a smoothing augmented Lagrangian method for solving a general class of nonsmooth and nonconvex constrained optimization problems. We show that, if the sequence of penalty parameters is bounded, then any accumulation point is a Karush-Kuch-Tucker (KKT) point of the nonsmooth optimization problem. The smoothing augmented Lagrangian method is used to solve the combined problem. Numerical experiments show that the algorithm is efficient for solving the simple bilevel program.     

Detection of maximum loadability limits and weak buses using Chaotic PSO considering security constraints

In the current research chaotic search is used with the optimization technique for solving non-linear complicated power system problems because Chaos can overcome the local optima problem of optimization technique. Power system problem, more specifically voltage stability, is one of the practical examples of non-linear, complex, convex problems. Smart grid, restructured energy system and socio-economic development fetch various uncertain events in power systems and the level of uncertainty increases to a great extent day by day. In this context, analysis of voltage stability is essential. The efficient method to assess the voltage stability is maximum loadability limit (MLL). MLL problem is formulated as a maximization problem considering practical security constraints (SCs). Detection of weak buses is also important for the analysis of power system stability. Both MLL and weak buses are identified by PSO methods and FACTS devices can be applied to the detected weak buses for the improvement of stability. Three particle swarm optimization (PSO) techniques namely General PSO (GPSO), Adaptive PSO (APSO) and Chaotic PSO (CPSO) are presented for the comparative study with obtaining MLL and weak buses under different SCs. In APSO method, PSO-parameters are made adaptive with the problem and chaos is incorporated in CPSO method to obtain reliable convergence and better performances. All three methods are applied on standard IEEE 14 bus, 30 bus, 57 bus and 118 bus test systems to show their comparative computing effectiveness and optimization efficiencies.     

A primal-dual interior point method for optimal zero-forcing beamformer design under per-antenna power constraints

In this paper, we consider an optimal zero-forcing beamformer design problem in multi-user multiple-input multiple-output broadcast channel. The minimum user rate is maximized subject to zero-forcing constraints and power constraint on each base station antenna array element. The natural formulation leads to a nonconvex optimization problem. This problem is shown to be equivalent to a convex optimization problem with linear objective function, linear equality and inequality constraints and quadratic inequality constraints. Here, the indirect elimination method is applied to reduce the convex optimization problem into an equivalent convex optimization problem of lower dimension with only inequality constraints. The primal-dual interior point method is utilized to develop an effective algorithm (in terms of computational efficiency) via solving the modified KKT equations with Newton method. Numerical simulations are carried out. Compared to algorithms based on a trust region interior point method and sequential quadratic programming method, it is observed that the method proposed is much superior in terms of computational efficiency.     

Convexification, Concavification and Monotonization in Global Optimization

We show in this paper that via certain convexification, concavification and monotonization schemes a nonconvex optimization problem over a simplex can be always converted into an equivalent better-structured nonconvex optimization problem, e.g., a concave optimization problem or a D.C. programming problem, thus facilitating the search of a global optimum by using the existing methods in concave minimization and D.C. programming. We first prove that a monotone optimization problem (with a monotone objective function and monotone constraints) can be transformed into a concave minimization problem over a convex set or a D.C. programming problem via pth power transformation. We then prove that a class of nonconvex minimization problems can be always reduced to a monotone optimization problem, thus a concave minimization problem or a D.C. programming problem.     

A novel neural network based on NCP function for solving constrained nonconvex optimization problems

This article presents a novel neural network (NN) based on NCP function for solving nonconvex nonlinear optimization (NCNO) problem subject to nonlinear inequality constraints. We first apply the p‐power convexification of the Lagrangian function in the NCNO problem. The proposed NN is a gradient model which is constructed by an NCP function and an unconstrained minimization problem. The main feature of this NN is that its equilibrium point coincides with the optimal solution of the original problem. Under a proper assumption and utilizing a suitable Lyapunov function, it is shown that the proposed NN is Lyapunov stable and convergent to an exact optimal solution of the original problem. Finally, simulation results on two numerical examples and two practical examples are given to show the effectiveness and applicability of the proposed NN. © 2015 Wiley Periodicals, Inc. Complexity 21: 130–141, 2016     

用最小范数法解三峡梯级水电站短期经济调度问题

本文主要研究三峡梯级水电站与华中、华东和川东电网联网的短期经济调度问题,利用泛函分析和运筹学相结合的方法建立了三峡梯级水电站日负荷最优分配的数学模型。本文扩充和推广了Hawary和Christensen的最小范数法用来求解这个具有等式和不等式约束的高维非线性含时滞的动态最优化问题,最优策略由一组动态的非线性代数、微分方程确定。引入适当的变量并进行适当化简,最终可将三峡梯级水电系统的经济调度问题转化为一个最小范数问题,并给出了最优解的具体表达式.用Lagrange乘子和Kuhn-Tucker乘子将约束条件并入目标函数中形成一个增广价格函数。通过变换可将该无约束优化问题转化为求解非线性代数方程组的问题。本文选用Fletcher-Reeves共轭梯度法求解无约束极值问题.在IBM-PC型微机上进行了试算。试算结果表明用最小范数法求解三峡梯级水电站日负荷最优分配问题是完全可行的,梯级水耗率有明显下降,能获得一定的经济效益。